Setup and Rule Diagrams

[Administrator]

Setup and Rule Diagram Explanation

This is a Grouping Game: Defined-Moving, Balanced, Numerical Distribution.

On the surface, this game appears fairly easy: five pieces of mail addressed to three different housemates. However, there is a great deal of uncertainty because number of pieces of mail each housemate receives is not fixed.

With only five pieces of mail for the three housemates, and with each housemate receiving at least one piece of mail, there are only two possible numerical distributions in this game:


3 - 1 - 1: one housemate receives three pieces of mail, and each of the other housemates receives one piece of mail.

2 - 2 - 1: two housemates receives two pieces of mail each, and the other housemate receives one piece of mail.

The last rule ties into these two distributions by establishing that the housemate receiving F must be in the group of 3 in the 3-1-1 distribution, or in one of the groups of 2 in the 2-2-1 distribution.

The other two rules are fairly generic. The first rule establishes two Not Laws on G, and leaves G with only three options for mail: F, P, and/or S. This rule also establishes that L and M will always be addressed to J or R. This has important consequences when paired with the second rule.

The second rule is conditional, and can be diagrammed as follows:

• LR PJ

From this rule, we can deduce that when L is addressed to R, and consequently P is addressed to J, that F or S is addressed to G:

• LR PJ F/SG

In this chain relationship, F, or F and S, must be addressed to G. At a minimum, S must always be addressed to G since addressing F to G would require S to be addressed to G as well, per the actions of the last rule.

The rules and relationships above can be compiled to form our main diagram:

June 06_M12_game#2_L5_explanations_game#2_setup_diagram_1.png

Another important deduction in this game is that either L or P (or both) must be addressed to Jana. This is a function of the contrapositive of the second rule: if P is not addressed to Jana, then L cannot be addressed to Rini. But, since L can only be addressed to Jana or Rini (and not Georgette, thanks to the first rule), it logically follows that if P is not addressed to Jana, then L must be addressed to Jana (PJ LJ). And inversely, if L is not addressed to Jana, then P must be (LJ PJ).

With the information in the setup, we are ready for the questions.

[saygracealways]

Hi Powerscore!

Could you please explain why this game would be categorized as "Balanced"?

I understand that it's a Defined-Moving game because all five of the mail pieces must be selected, and the numerical distribution among the three bases (Georgette, Jana and Rini) isn't fixed. However, I'm wondering if the game should be categorized as "Unbalanced-Overloaded" instead because there's 5 pieces of mail to go into 3 bases?

Thank you!

[Jon Denning]

Hi saygrace - thanks so much for posting!

The idea in this game that balances it is the fact that we know all five pieces of mail are being used exactly once, so there's no uncertainty to the numbers themselves (despite not knowing exactly what the distribution will be, hence the overloaded label). I get that we have more mail than people, and in that regard there is in fact a mismatch...but typically we tend to discuss balance more in the sense of moving/changing amounts than in simple terms of 5:3 or vice versa, and that definitive selection is what prompted the labeling. (An argument could certainly be made for labeling it otherwise though, I'll grant...so you raise a great point! Games are sometimes slippery that way)

This also introduces an interesting notion, in my opinion, and one that you're savvy to have spotted: the real key with numbers is seeing distributions and uncertainties, and while there's no uncertainty here about what the numbers will be—exactly five and exactly three, hence the concept of balance—there are distribution options and an overloaded variable set, and those will undoubtedly control the game at its heart. If that becomes the central focus as you first approach it you'll be in great shape

I hope that helps!

[glasann]

Is the reason you wouldn't create templates around L w/ J and L w/ R simply because you wouldn't be able to fill in much with the former template? The latter does seem to be helpful since you seem to be able to fill in everything apart from M (which could be with J or L).

thanks!

[Christen Hammock]

Hey Rademaker!

If drawing out a few scenarios during the beginning of the game is helpful to you, definitely do it! That particular template isn't necessary to solve the game, but it will definitely help you learn more about the game.

Christen

[nzLSAT]

Hello,

I am a little confused in the beginning steps on how you were able to make the inference of"From this rule, we can deduce that when L is addressed to R, and consequently P is addressed to J, that F or S is addressed to G: LR -> PJ -> F/SG." I don't think I quite understand how you were able to get this inference from the "If Lr -> Pj" rule.

Does have Lr and Pj mean that Rini ONLY has a letter and Jana ONLY has a postcard? Could it be that they do not receive anything else?

Also, is the contrapositive to the rule "If LR -> Pj" turn into "If Jana does not receive a postcard, then Rini does not receive the letter?"

[Rachael Wilkenfeld]

Hi nzLSAT,

First, you got the contrapositive exactly right at the end! Way to go.

Second, the F/S to G deduction is just a matter of elimination. G has to receive something. If J receives P and R receives L, then they aren't available to go to G. M never goes to G per the rules. So that just leaves F/S to go to G.

And Lr and Pj aren't saying those are the ONLY items they receive. There could be others.

Hope that helps!